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A relaxation theorem for partially observed stochastic control on Hilbert space

N.U. Ahmed (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that...

A Remark on Variational Principles of Choban, Kenderov and Revalski

Adrian Królak (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.

A Riccati equation arising in a boundary control problem for distributed parameters

Franco Flandoli (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si prova resistenza locale della soluzione di una equazione di Riccati che si incontra in un problema di controllo ottimale. In ipotesi di regolarità per il costo si prova resistenza globale. Il problema astratto considerato è il modello di alcuni problemi di controllo ottimale governati da equazioni paraboliche con controllo sulla frontiera.

Abstract variational problems with volume constraints

Marc Oliver Rieger (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

Abstract variational problems with volume constraints

Marc Oliver Rieger (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

An active set strategy based on the augmented Lagrangian formulation for image restoration

Kazufumi Ito, Karl Kunisch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by...

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